Table 6 The comparison of the \(l^{2}\)-norm and the \(l^{\infty}\)-norm when \(\tau= h_{x} =h_{y} \) for \(\mathcal{O}(h_{x}^{2} + h_{y}^{2})\) standard central difference scheme, at different values of the step size (for \(N = 4,8,16,32,64,128\)) in the x and y directions

\(\frac{1}{4}\)

1.4022e–003

4.4825e–002

\(\frac{1}{8}\)

8.2045e–004

0.7733

3.1211e–003

\(\frac{1}{16}\)

2.0868e–004

1.9751

1.5901e–003

\(\frac{1}{32}\)

5.2198e–005

1.9992

1.1661e–003

\(\frac{1}{64}\)

1.3050e–005

1.9999

6.8089e–004

\(\frac{1}{128}\)

3.2626e–006

2.0000

3.6604e–004